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<div>Suppose that A has high approval or high first place support .... whatever is likely to put him at the good end of the agenda ... but knows that C has the broad & deep support necessary to be the sincere CW... in particular beating A pairwise.. and that
there is some candidate B that A beats pairwise ... and the sincere preference order of the A faction is (mostly) A>C>B, (among these 3 major candidates)</div>
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<div>Then A (emboldened by his presumed favorable agenda standing) gets the bright idea of convincing his supporters to bury C under B to create an artificial Condorcet cycle A>B>C>A.</div>
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<div>Without this artificial cycle C would win no matter the agenda order ... but now A, at the top of the agenda has a good chance. In fact, the three members of this Smith set are the only possible winners under ISDA (Independence from Smith Dominated Alternatives).</div>
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<div>When Smith has only three candidates, some agenda based methods, like SPE and ABL always elect the cycle member with the best agenda position... in this case A.</div>
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<div>Another method DMC (Definite Majority Choice), elects the item in the worst agenda position that pairwise beats every item in a higher position ... which in this case is A if the agenda order of favor is (1) C<B<A, but is C if the order is (2) B<C<A.</div>
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<div>How about ABB?</div>
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<div>In case (1) C is the first bank deposit, and B is the last, hence the winner.</div>
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<div>In case (2) B is the first deposit and A is the last, hence winner.</div>
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<div>Both DMC and ABB make A's gambit somewhat risky, and if C's supporters take the standard CW precaution of truncating below C, then A's agenda status becomes least favorable of the three, in which case A loses by any reasonable agenda based method.</div>
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<div>How do DMC and ABB compare under Chicken attack?</div>
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<div>49 B</div>
<div>26 C>A</div>
<div>25 A (sincere is A>B)</div>
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<div>Given implicit approval as the agenda setting criterion, A has the favored agenda spot, which makes A win under SPE and ABL. </div>
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<div>Candidate C has the worst agenda position, so the agenda order is C<B<A, which makes Chicken attacker A win under DMC.</div>
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<div>So our last hope is ABB. It comes through by electing B... fortunately NOT electing the most favored Banks agenda item!</div>
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<div>[When Smith is a triple, Banks = Smith]</div>
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<div>The very thing that turned me off about ABB years ago (when it was just TACC) made it impervious to Chicken!</div>
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<div>ABB (Agenda Based Banks) looks Better and Better Actually (BBA).</div>
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<div>... Forest (sharing Sue's phone) </div>
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<div dir="auto" style="font-size:85%; color:#575757">Sent from my MetroPCS 4G LTE Android Device</div>
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<div>-------- Mensaje original --------</div>
<div>De: Kristofer Munsterhjelm <km_elmet@t-online.de> </div>
<div>Fecha: 2/8/21 2:13 p. m. (GMT-08:00) </div>
<div>A: Susan Simmons <suzerainsimmons@outlook.com>, election-methods@lists.electorama.com
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<div>Asunto: Re: [EM] Agenda Based Banks </div>
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<div class="PlainText">On 02.08.2021 21:31, Susan Simmons wrote:<br>
> It turns out that this method as it stands is not monotonic, but if you<br>
> omit the downward part, then the remaining simpler version is monotonic:<br>
> <br>
> First initialize a set named "TheBank" with the most promising agenda item. <br>
> <br>
> Then, as long as even one agenda item pairwise beats every member<br>
> ofTheBank, deposit the least promising of these into TheBank. <br>
> <br>
> Elect the final deposit.<br>
> <br>
> This simple Banks compliant method is a generalization of TACC (Total<br>
> Approval Chain Climbing).<br>
> <br>
> The only thing I don't like about it is that even when the most<br>
> promising agenda item is in the Banks set, as likely as not it will<br>
> elect a different member of that set. My tweak was designed to overcome<br>
> that "defect" while preserving Banks efficiency. But it's not worth the<br>
> loss of monotonicity. <br>
> <br>
> Furthermore, it may turn out that the supposed "defect" actually confers<br>
> burial resistance ... for example ...<br>
> <br>
> 45 A>B (sincere A>C)<br>
> 25 B>C<br>
> 30 C>A<br>
> <br>
> Ballot pairwise beat cycle: A>B>C>A<br>
> <br>
> Agenda: C<B<A<br>
> (based on implicit approval, for example)<br>
<br>
That feels like it's a general feature. Consider e.g. Benham with a<br>
preset ordering as an agenda method (remove the loser until there's a CW<br>
among the remaining candidates). Then raising W puts more candidates<br>
between W and the end of the list, which means that in the worst case,<br>
more candidates have to be eliminated before W wins.<br>
<br>
It seems like there's some kind of tension where, on the one hand, being<br>
ranked more highly should be advantageous (which it is if the pairwise<br>
preferences don't change, because it saves W from early elimination),<br>
but on the other hand, being ranked more highly with pairwise<br>
preferences changing has a higher chance of being detrimental (because<br>
more candidates have to be eliminated before W becomes a CW).<br>
<br>
-km<br>
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